Question

Equal mass of Zn metal and iodine are mixed together and the iodine is completely converted to \[Zn{{I}_{2}}\]. What fraction of mass of the original Zn remains unreacted?
(Write numerical value up to 2 digits only after decimal point as for 0.19, write 19)

Answer 1

Hint: The answer to this question is obtained through the application of Proust’s law or as it is more popularly known, the law of constant proportions. Think about how this law is applicable in this question.

Complete step-by-step answer:
Let us first define the law of constant proportions, a law which is integral to the solution to this question.
In chemistry, the law of definite proportion, sometimes called Proust's law, or law of constant composition states that a given chemical compound always contains its component elements in fixed ratio (by mass) and does not depend on its source and method of preparation. For example, oxygen makes up about \[\dfrac{8}{9}~\] of the mass of any sample of pure water, while hydrogen makes up the remaining \[\dfrac{1}{9}~\] of the mass. Along with the law of multiple proportions, the law of definite proportions forms the basis of stoichiometry.
With this in mind, let us now attempt to solve this question,
The molar masses of Zn and iodine are 65.39 g/mol and 253.8 g/mol respectively.
Let us assume that 253.8 g of zinc is mixed with 253.8 g of iodine.
The number of moles of \[Zn~=\dfrac{253.8}{65.39}=3.88.\]
The number of moles of \[Iodine~=\dfrac{253.8}{253.8}=1\]
The balanced chemical equation is
\[Zn+{{I}_{2}}\rightleftharpoons Zn{{I}_{2}}\]
Applying the law of constant proportions,
1 mole of Zn reacts with 1 mole of iodine.
The number of moles of unreacted Zn are 3.88 – 1 = 2.88
The mass of unreacted zinc is 65.39 × 2.88 = 188.41g.
The percentage of zinc unreacted is thus \[\dfrac{188.41}{253.8}\times 100=74~%\]
Therefore, the answer to this question here is 74.

Note: Be very careful of the difference between the laws of constant and multiple proportions as using the latter will result in a completely wrong answer, both conceptually and mathematically. Also, be extremely wary of the reaction equation between Zn and I as its knowledge is key towards answering this question.